Answer:
The value of cos Ф is ± ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
Step-by-step explanation:
There are important rules for sin Ф and cos Ф
∵ sin Ф = ![\frac{\sqrt{3}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D)
∴ sin²Ф = ![(\frac{\sqrt{3}}{2})^{2}](https://tex.z-dn.net/?f=%28%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%29%5E%7B2%7D)
∴ sin²Ф = ![\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D)
→ By using the third rule above
∵ cos²Ф = 1 - sin²Ф
∴ cos²Ф = 1 - ![\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D)
∴ cos²Ф = ![\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D)
→ Take square root for both sides
∴ cos Ф = ± ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
∴ The value of cos Ф is ± ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
<u>Where is the triangle "JKL"? The one is the picture is "EFGH"</u>
3 gallons minus 1 quart (I'm assuming), is 2 gallons 3 quarts.
18 is the answer.1/8 is 6 so all you need to do is find that and multiply it by the numerator
<u><em>Answer</em></u>
length: 8 inch and width: 5 inch
<u><em>Explanation</em></u>
Let width be x,
then the length: x + 3
solve:
![\sf (x+3)(x) = 40](https://tex.z-dn.net/?f=%5Csf%20%28x%2B3%29%28x%29%20%3D%2040)
![\sf x^2+3x = 40](https://tex.z-dn.net/?f=%5Csf%20x%5E2%2B3x%20%3D%2040)
![\sf x^2+3x-40=0](https://tex.z-dn.net/?f=%5Csf%20x%5E2%2B3x-40%3D0)
![\sf x^2+8x-5x-40=0](https://tex.z-dn.net/?f=%5Csf%20x%5E2%2B8x-5x-40%3D0)
![\sf x(x+8)-5(x+8)=0](https://tex.z-dn.net/?f=%5Csf%20x%28x%2B8%29-5%28x%2B8%29%3D0)
![\sf (x-5)(x+8)=0](https://tex.z-dn.net/?f=%5Csf%20%28x-5%29%28x%2B8%29%3D0)
![\sf x = 5 \ or \ -8](https://tex.z-dn.net/?f=%5Csf%20x%20%3D%205%20%5C%20or%20%5C%20%20-8)
- As width cannot be negative, width will be 5.
Find for length:
![\sf x + 3](https://tex.z-dn.net/?f=%5Csf%20x%20%2B%203)
![\sf 5+ 3](https://tex.z-dn.net/?f=%5Csf%20%205%2B%203)
![\sf 8](https://tex.z-dn.net/?f=%5Csf%208)